Question: Simplify the following expression: $p = \dfrac{7q^2 + 49q - 210}{q - 3} $
Solution: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $7$ , so we can rewrite the expression: $ p =\dfrac{7(q^2 + 7q - 30)}{q - 3} $ Then we factor the remaining polynomial: $q^2 + {7}q {-30} $ ${-3} + {10} = {7}$ ${-3} \times {10} = {-30}$ $ (q {-3}) (q + {10}) $ This gives us a factored expression: $\dfrac{7(q {-3}) (q + {10})}{q - 3}$ We can divide the numerator and denominator by $(q + 3)$ on condition that $q \neq 3$ Therefore $p = 7(q + 10); q \neq 3$